Evaluate log b {square root of 10b}, given that log b 2 = 0.3562 and

Question

log b 5 = 0.8271 (sorry I had no clue how to type this in math format!)

Answer 1

I am not sure if I interpret your question correctly.
Given log_b2 = 0.3562 and
log_b5 = 0.8271,
evaluate log_b{square-root of 10_b};

log_b{square-root of 10_b}
= log_b{square-root of 2_b*5_b}
=(1/2)log_b(10_b)
=(1/2)(1)
=0.5
since log_b10_b = b for any b.
However, if the number 10 is replaced by 10 to the base 10, we proceed slightly differently:
log_b{square-root of 10}
=(1/2)log_b(10)
= (1/2)log_b(2*5)
= (1/2)(log_b(2)+log_b(5))
= (1/2)(0.3562+0.8271)
=0.5916

Answer 2

I saw the question this way

log_b (√(10b))
= 1/2(log_b(10b))
= 1/2(log_b5 + log_b2 + log_bb)
= 1/2(.8271 + .3562 + 1)
= 1.0917

Answer 3

The second answer is the correct answer! Thanks to you both I am on my way to the final

Shellie